Strategic Learning for Disturbance Rejection in Multi-Agent Systems: Nash and Minmax in Graphical Games

This article investigates the optimal control problem with disturbance rejection for discrete-time multi-agent systems under cooperative and non-cooperative graphical games frameworks. Given the practical challenges of obtaining accurate models, Q-function-based policy iteration methods are proposed to seek the Nash equilibrium solution for the cooperative graphical game and the distributed minmax solution for the non-cooperative graphical game. To implement these methods online, two reinforcement learning frameworks are developed, an actor-disturber-critic structure for the cooperative graphical game and an actor-adversary-disturber-critic structure for the non-cooperative graphical game. The stability of the proposed methods is rigorously analyzed, and simulation results are provided to illustrate the effectiveness of the proposed methods.